10.5 The for Statement

The for statement makes it more convenient to count iterations of a
loop. The general form of the for statement looks like this:

for var = expressionbody
endfor

where body stands for any statement or list of statements,
expression is any valid expression, and var may take several
forms. Usually it is a simple variable name or an indexed variable. If
the value of expression is a structure, var may also be a
vector with two elements. See Looping Over Structure Elements, below.

The assignment expression in the for statement works a bit
differently than Octave’s normal assignment statement. Instead of
assigning the complete result of the expression, it assigns each column
of the expression to var in turn. If expression is a range,
a row vector, or a scalar, the value of var will be a scalar each
time the loop body is executed. If var is a column vector or a
matrix, var will be a column vector each time the loop body is
executed.

The following example shows another way to create a vector containing
the first ten elements of the Fibonacci sequence, this time using the
for statement:

This code works by first evaluating the expression 3:10, to
produce a range of values from 3 to 10 inclusive. Then the variable
i is assigned the first element of the range and the body of the
loop is executed once. When the end of the loop body is reached, the
next value in the range is assigned to the variable i, and the
loop body is executed again. This process continues until there are no
more elements to assign.

Within Octave is it also possible to iterate over matrices or cell arrays
using the for statement. For example consider

disp ("Loop over a matrix")
for i = [1,3;2,4]
i
endfor
disp ("Loop over a cell array")
for i = {1,"two";"three",4}
i
endfor

In this case the variable i takes on the value of the columns of
the matrix or cell matrix. So the first loop iterates twice, producing
two column vectors [1;2], followed by [3;4], and likewise
for the loop over the cell array. This can be extended to loops over
multi-dimensional arrays. For example:

a = [1,3;2,4]; c = cat (3, a, 2*a);
for i = c
i
endfor

In the above case, the multi-dimensional matrix c is reshaped to a
two-dimensional matrix as reshape (c, rows (c),
prod (size (c)(2:end))) and then the same behavior as a loop over a two
dimensional matrix is produced.

Although it is possible to rewrite all for loops as while
loops, the Octave language has both statements because often a
for loop is both less work to type and more natural to think of.
Counting the number of iterations is very common in loops and it can be
easier to think of this counting as part of looping rather than as
something to do inside the loop.